Metallicity relations in LMC and SMC from the slope of Red Giant Branch stars in globular clusters

Red giants are an excellent tool for probing the history of star formation and subsequent metallicity evolution in the galaxies. The well-defined red giant branch (RGB) stars of the globular clusters can be used to determine their slopes and to calibrate the RGB slope parameters, age, and metallicity relations. We obtained deep near-IR $JHK$ stellar photometry of 23 LMC/SMC globular clusters. The cluster sample covers a wide range in metallicities $(-1.76<[\mathrm{F}\mathrm{e}\mathrm{/}\mathrm{H}]<-0.32)$ and ages $(0.6\mathrm{G}\mathrm{y}\mathrm{r}<t<14\mathrm{G}\mathrm{y}\mathrm{r})$. The slope of the RGBs of each cluster was calculated and used to derive the relations between slope-age-metallicity. We have found that the RGB slope do not shows any statistically significant age dependence. The young and old clusters are found to be distributed differently in RGB slope-metallicity space, and the younger populations show a slightly less steep RGB slope dependence than the whole cluster sample. The population of the younger clusters shows a negative slope, whereas the older clusters show a positive slope.